It is believed the ban follows a move by a Turkish court in response to a case filed by Turkish Union of Music Producers (MÜYAP) in order to protect music rights, say reports.
The ban could represent a significant blow to both websites. According to a recent ComScore report, Turkey has 7th largest and most engaged online audience in Europe with 27m internet users.
The May report said: "The online population of Turkey far surpasses the rest of Europe in terms of time spent and content consumed per person."
Separately, in the UK pop singer James Blunt has backed Lily Allen's call for internet users who illegally share music files to be disconnected from the web.
Allen was supporting Business Secretary Lord Mandelson's plans to clamp down on illegal file-sharers.
Blunt has described ISP's who permit file-sharing from sites such as BitTorrent and The Pirate Bay of "handling stolen goods".
The strength of Blunt's attack suggests there are deep divisions within the music industry over how it should deal with users who swap songs for free.
Last week, Allen laid into "rich and successful artists" such as Ed O'Brien, of Radiohead, and Nick Mason, the Pink Floyd drummer, who recently came out against Mandelson's ideas, arguing that file-sharing had some beneficial effects for artists.